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A177375 Triangle t(n,k): the coefficient [x^k] of the series (1+x)^n + 2*n*x*(1+x)^(n-2), in row n, column k.

%I A177375 #6 May 19 2013 23:59:41
%S A177375 1,1,3,1,6,1,1,9,9,1,1,12,22,12,1,1,15,40,40,15,1,1,18,63,92,63,18,1,
%T A177375 1,21,91,175,175,91,21,1,1,24,124,296,390,296,124,24,1,1,27,162,462,
%U A177375 756,756,462,162,27,1,1,30,205,680,1330,1652,1330,680,205,30,1
%N A177375 Triangle t(n,k): the coefficient [x^k] of the series (1+x)^n + 2*n*x*(1+x)^(n-2), in row n, column k.
%C A177375 Row sums are in A001792.
%e A177375 1;
%e A177375 1, 3;
%e A177375 1, 6, 1;
%e A177375 1, 9, 9, 1;
%e A177375 1, 12, 22, 12, 1;
%e A177375 1, 15, 40, 40, 15, 1;
%e A177375 1, 18, 63, 92, 63, 18, 1;
%e A177375 1, 21, 91, 175, 175, 91, 21, 1;
%e A177375 1, 24, 124, 296, 390, 296, 124, 24, 1;
%e A177375 1, 27, 162, 462, 756, 756, 462, 162, 27, 1;
%e A177375 1, 30, 205, 680, 1330, 1652, 1330, 680, 205, 30, 1;
%p A177375 A177375 := proc(n,k)
%p A177375     (1+x)^n+2*n*x*(1+x)^(n-2) ;
%p A177375     coeftayl(%,x=0,k)
%p A177375 end proc: # _R. J. Mathar_, May 19 2013
%t A177375 p[x, 0, q_] := 1; p[x, 1, q_] := x + 1;
%t A177375 p[x_, n_, q_] := p[x, n, q] = (1 + x)^n + 2*q*n*x*(1 + x)^(n - 2);
%t A177375 Table[Flatten[Table[CoefficientList[p[x, n, q], x], {n, 0, 10}]], {q, 1, 10}]
%Y A177375 Cf. A162246
%K A177375 nonn,tabl
%O A177375 0,3
%A A177375 _Roger L. Bagula_, May 07 2010